Ratio of Mean to Median

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As stated before, median-of-medians is used as a pivot selection strategy in the quickselect algorithm, which in pseudocode looks as follows. Be careful to handle left, right and n when wholesumfamilyfarms.info: Selection algorithm. The Medes were formerly called by everyone Arians, but when the Colchian woman Medea came from Athens to the Arians, they changed their name, like the Persians [did after Perses, son of Perseus and Andromeda]. This is the Medes' own account of themselves. ”.

These tribes expanded their control over larger areas. Subsequently, the boundaries of Media changed over a period of several hundred years. But the significance of Iranian elements in these regions were established from the beginning of the second half of the 8th century BC. This period of migration coincided with a power vacuum in the Near East with the Middle Assyrian Empire — BC , which had dominated northwestern Iran and eastern Anatolia and the Caucasus , going into a comparative decline.

This allowed new peoples to pass through and settle. In addition Elam , the dominant power in Iran, was suffering a period of severe weakness, as was Babylonia to the west.

In western and northwestern Iran and in areas further west prior to Median rule, there is evidence of the earlier political activity of the powerful societies of Elam, Mannaea, Assyria and Urartu. From the 10th to the late 7th centuries BC, the western parts of Media fell under the domination of the vast Neo-Assyrian Empire based in northern Mesopotamia , which stretched from Cyprus in the west, to parts of western Iran in the east, and Egypt and the north of the Arabian Peninsula.

During the reign of Sinsharishkun — BC , the Assyrian empire, which had been in a state of constant civil war since BC, began to unravel. Neo-Assyrian dominance over the Medians came to an end during the reign of Median King Cyaxares , who, in alliance with King Nabopolassar of the Neo-Babylonian Empire , attacked and destroyed the strife-riven empire between and BC.

After the fall of Assyria between BC and BC, a unified Median state was formed, which together with Babylonia, Lydia , and ancient Egypt became one of the four major powers of the ancient Near East. Cyaxares was succeeded by his son King Astyages. In BC, Cyrus finally won a decisive victory resulting in Astyages' capture by his own dissatisfied nobles, who promptly turned him over to the triumphant Cyrus.

The list of Median rulers and their period of reign compiled according to two sources. Firstly, Herodotus who calls them "kings" and associates them with the same family. A combined list stretching over years is thus:. However, not all of these dates and personalities given by Herodotus match the other near eastern sources. In Herodotus book 1, chapters 95— , Deioces is introduced as the founder of a centralised Median state.

He had been known to the Median people as "a just and incorruptible man" and when asked by the Median people to solve their possible disputes he agreed and put forward the condition that they make him "king" and build a great city at Ecbatana as the capital of the Median state.

Greek references to "Median" people make no clear distinction between the "Persians" and the "Medians"; in fact for a Greek to become "too closely associated with Iranian culture" was "to become Medianized, not Persianized". Median people spoke the Median language, which was an Old Iranian language. Strabo 's Geographica finished in the early first century mentions the affinity of Median with other Iranian languages: No original deciphered text has been proven to have been written in the Median language.

It is suggested that similar to the later Iranian practice of keeping archives of written documents in Achaemenid Iran, there was also a maintenance of archives by the Median government in their capital Ecbatana. There are examples of "Median literature" found in later records. One is according to Herodotus that the Median king Deioces, appearing as a judge, made judgement on causes submitted in writing. There is also a report by Dinon on the existence of "Median court poets".

Words of Median origin appear in various other Iranian dialects, including Old Persian. A feature of Old Persian inscriptions is the large number of words and names from other languages and the Median language takes in this regard a special place for historical reasons.

There are very limited sources concerning the religion of Median people. Primary sources pointing to religious affiliations of Medes found so far include the archaeological discoveries in Tepe Nush-e Jan, personal names of Median individuals, and the Histories of Herodotus.

The archaeological source gives the earliest of the temple structures in Iran and the "stepped fire altar" discovered there is linked to the common Iranian legacy of the "cult of fire". Herodotus mentions Median Magi as a Median tribe providing priests for both the Medes and the Persians.

They had a "priestly caste" which passed their functions from father to son. They played a significant role in the court of the Median king Astyages who had in his court certain Medians as "advisers, dream interpreters, and soothsayers".

Classical historians "unanimously" regarded the Magi as priests of the Zoroastrian faith. From the personal names of Medes as recorded by Assyrians in 8th and 9th centuries BC there are examples of the use of the Indo-Iranian word arta- lit.

Diakonoff believes that "Astyages and perhaps even Cyaxares had already embraced a religion derived from the teachings of Zoroaster" which was not identical with doctrine of Zarathustra and Mary Boyce believes that "the existence of the Magi in Media with their own traditions and forms of worship was an obstacle to Zoroastrian proselytizing there". It has also been suggested [ by whom?

Russian historian and linguist Vladimir Minorsky suggested that the Medes, who widely inhabited the land where currently the Kurds form a majority, might have been forefathers of the modern Kurds. He also states that the Medes who invaded the region in the eighth century BC, linguistically resembled the Kurds. This view was accepted by many Kurdish nationalists in the twentieth century. However, Martin van Bruinessen , a Dutch scholar, argues against the attempt to take the Medes as ancestors of the Kurds.

Contemporary linguistic evidence has challenged the previously suggested view that the Kurds are descendants of the Medes.

It can come as a shock to realize that there is on occasion no finger available to make this possible. In a sense we can argue that similar principles apply to the interpretation of these transcriptions.

As one would expect of Russian pianist—composers of this epoch, the emphasis is on the monumental grandeur of the music. The discreet piping of the baroque organ was probably quite unknown to them.

By inclination he eschews grandiloquence and elaboration in favour of intimate meditation. A pupil of Nicholas Rubinstein and Tchaikovsky, later of Liszt in Weimar, he was in turn one of the teachers of his cousin Rachmaninov.

His reputation as a pianist and conductor of the highest distinction seems to have been unquestioned. After emigrating to New York in his public profile diminished but he remained a figure revered by his pupils and colleagues.

In all of his transcriptions his aristocratic pianistic pedigree is evidenced by the fastidious perfectionism of his writing. Nothing is left to chance; the scores, while superficially simple, are replete with meticulous pedal markings and copious fingerings which have little to do with keyboard manipulation but everything to do with achieving a distinctive sonority and phrasing.

In general he seems to have been attracted to this music more by its noble melody and flawless harmonic paragraphs than by its intricacy of counterpoint or dramatic power. The ebb and flow of harmonic tension in the sombre Adagio from the violin sonata in F minor is realized by means of a scrupulously plotted dynamic graph that would be frowned upon today, yet it captures the inexorable unity of the piece to perfection.

The inherently subjective nature of our cherished musicological objectivity surfaces in the Andante from the A minor solo violin sonata. In the original Bach-Gesellschaft edition there was a rather weak keyboard transcription of the whole sonata, but later research has pronounced it spurious.

The Siciliano from the flute sonata in E flat major has been the object of several piano transcriptions Alkan, Kempff, Friedman and others as well as suffering the indignity of issuing as muzak from countless elevators and hotel lobbies.

Alexander Fyodorovich Goedicke — numbers among a sizeable group of fine Russian musicians who virtually disappeared from view in the Soviet age, displaying neither the rebellious nature to attract the attention of refuseniks or Westerners nor the mindless adherence to political diktats which might have attracted state patronage and later, probably, infamy.

He pursued an unspectacular career on four fronts as composer, pianist, organist and teacher. It seems a bizarre paradox that a fine organist should lavish so much care and imagination on concert transcriptions for the piano. Contrary to Western myth, the church was not totally suppressed under the communist regime but it was, of course, stripped of its hitherto formidable political power.

Consequently it lacked the wherewithal, the expertise and possibly the will to maintain its organs in a usable state of repair. It is conceivable that Goedicke turned to the piano in sheer frustration but more likely that these transcriptions were simply a labour of love.

His fondness for widespread textures tests the agility of hand and arm almost to the limit at times, but the intrinsically pianistic nature of their deployment ensures that it presents no real impediment to the indomitable energy of the music. With admirable tact and discretion, he leaves the devotional simplicity of the Prelude almost untouched.

Just as it seems to have come to a full and natural close there follows an improvisatory postlude. Such are the endlessly fascinating ambiguities of Bach. His most influential teacher was Karl Klindworth, a disciple of Wagner, which set him a little distant from the mainstream Russian tradition.

But he had the popular touch which so endeared him to his political masters and there is no denying the thrilling power of his climaxes. Perhaps, in our information-besotted age, we know too much. It is universally accepted that knowledge of itself brings neither wisdom nor understanding.

Die junge Generation musste sie sich entweder aneignen oder von ihr Abstand nehmen. For example, the worst case occurs when pivoting on the smallest element at each step, such as applying quickselect for the maximum element to already sorted data and taking the first element as pivot each time.

If one instead consistently chooses "good" pivots, this is avoided and one always gets linear performance even in the worst case. A "good" pivot is one for which we can establish that a constant proportion of elements fall both below and above it, as then the search set decreases at least by a constant proportion at each step, hence exponentially quickly, and the overall time remains linear. The median is a good pivot — the best for sorting, and the best overall choice for selection — decreasing the search set by half at each step.

Thus if one can compute the median in linear time, this only adds linear time to each step, and thus the overall complexity of the algorithm remains linear. The median-of-medians algorithm computes an approximate median, namely a point that is guaranteed to be between the 30th and 70th percentiles in the middle 4 deciles.

As stated before, median-of-medians is used as a pivot selection strategy in the quickselect algorithm, which in pseudocode looks as follows. Be careful to handle left , right and n when implementing.

It's better to use the same index for left , right and n to avoid handle index converting. There is a subroutine called partition that can, in linear time, group a list ranging from indices left to right into three parts, those less than a certain element, those equal to it, and those greater than the element a three-way partition.

The grouping into three parts ensures that the median-of-medians maintains linear execution time in a case of many or all coincident elements. Here is pseudocode that performs a partition about the element list[pivotIndex]:. Subroutine pivot is the actual median-of-medians algorithm. The partition5 subroutine selects the median of a group of at most five elements; an easy way to implement this is insertion sort , as shown below.

Note that pivot calls select ; this is an instance of mutual recursion.

Such simple precepts as beginning ornaments from above and on the beat are now so much the norm as to be instinctive. But the significance of Iranian elements in these regions were established from the beginning of the second half of the 8th century BC.